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We theoretically investigate in-medium three-body correlations inone-dimensional spinless fermions with antisymmetrized two- and three-bodyattractive interactions. By investigating the variational problem of three-bodystates above the Fermi sea, we illuminate the fate of the in-medium three-bodycluster states both in the special case with pure attractive three-bodyinteraction as well as in the case with the coexistence of two- and three-bodyinteractions. Our results testify that the fermion-dimer repulsion is canceledby including the three-body interactions, and stable three-body clusters can beformed. We further feature a phase diagram consisting of the $p$-wave Cooperpairing and Cooper tripling phases in a plane of $p$-wave two- and three-bodycoupling strengths.

Cooper pairing and tripling in one-dimensional spinless fermions with attractive two- and three-body forces